Question

The order and degree of the differential equation of all parabola whose axis is x-axis

• A. 2,1
• B. 2,2
• C. 1,2
• D. 1,1

Answer 1

The correct option is A 2,1

Equation of the required parabola is of the form $y^2=4a(x-h).$ Differentiating we have
$2y\frac{dy}{dx}=4a\Rightarrow y\frac{dy}{dx}=2a\Rightarrow {\left(\frac{dy}{dx}\right)}^2+y\frac{d^{2}y}{{dx}^2}=0$
The degree of this differential equation is $1$ and the order is $2$